\(=\left(x-y\right)^2+x=\left(25-5\right)^2+5=20^2+5=405\)

a: \(A=x\left(x+2\right)+y\left(y-2\right)-2xy\)

\(=x^2+2x+y^2-2y-2xy\)

\(=\left(x^2-2xy+y^2\right)+2\left(x-y\right)\)

\(=\left(x-y\right)^2+2\left(x-y\right)=7^2+2\cdot7=49+14=63\)

\(B=x^3-3xy\left(x-y\right)-y^3-x^2+2xy-y^2\)

\(=x^3-3x^2y+3xy^2-y^3-\left(x^2-2xy+y^2\right)\)

\(=\left(x-y\right)^3-\left(x-y\right)^2\)

\(=7^3-7^2=343-49=294\)

b: \(C=x^2+4y^2-2x+10+4xy-4y\)

\(=x^2+4xy+4y^2-2\left(x+2y\right)+10\)

\(=\left(x+2y\right)^2-2\left(x+2y\right)+10=5^2-2\cdot5+10=25\)

Ta có

N   =   x 3   +   3 x 2 y   +   3 x y 2   +   y 3   +   x 2   +   2 x y   +   y 2     =   ( x 3   +   3 x 2 y   +   3 x y 2   +   y 3 )   +   ( x 2   +   2 x y   +   y 2 )     =   ( x   +   y ) 3   +   ( x   +   y ) 2   =   ( x   +   y ) 2 ( x   +   y   +   1 )

Từ đề bài x = 10 – y ó x + y = 10. Thay x + y = 10 vào N = ( x   +   y ) 2 (x + y + 1) ta được

N = 10 2 (10 + 1) = 1100

Suy ra N > 1000 khi x = 10 – y

Đáp án cần chọn là: D

\(a,=5\left(x^2+2xy+y^2\right)-10y^2+5=5\left(x+y\right)^2-10y^2+5\\ =5\left(1+2\right)^2-10\cdot4+5=45-40+5=10\\ b,=7\left(x-y\right)-\left(x-y\right)^2=\left(x-y\right)\left(7-x+y\right)\\ =\left(2-2\right)\left(7-2+2\right)=0\)

b: \(=7\left(x-y\right)-\left(x-y\right)^2\)

\(=\left(x-y\right)\left(7-x+y\right)=0\)

dat A=x^2-2xy+y^2

A=x^2-xy-xy+y^2

A=x(x-y)-y(x-y)

A=(x-y)^2=5^2=25

do do A+5=25+5=30

nho **** cho tớ nhé

B=(x²-2xy+y²) + 5 = (x-y)² +5 = 5² +5 = 25+5 =30

a: \(=3x^4+3x^2y^2+2x^2y^2+2y^4+y^2\)

\(=\left(x^2+y^2\right)\left(3x^2+2y^2\right)+y^2\)

\(=3x^2+3y^2=3\)

b: \(=7\left(x-y\right)+4a\left(x-y\right)-5=-5\)

c: \(=\left(x-y\right)\left(x^2+xy+y^2\right)+xy\left(y-x\right)+3=3\)

d: \(=\left(x+y\right)^2-4\left(x+y\right)+1\)

=9-12+1

=-2

Ta có

ĐÁP ÁN C

\(A=x^2+y^2+\left(\dfrac{1}{2}\right)^2-2xy+2.\dfrac{1}{2}x-2.\dfrac{1}{2}.y+\dfrac{3}{4}\)

\(A=\left(x-y+\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)

\(A_{min}=\dfrac{3}{4}\) khi \(x-y+\dfrac{1}{2}=0\)

M =   99 - 100 - 1 99 + 1 + 100 = - 2 200 = - 1 100

Đáp án A

A   =   x 2   +   2 x y   +   y 2   –   4 x   –   4 y   +   1     =   ( x 2   +   2 x y   +   y 2 )   –   ( 4 x   +   4 y )   +   1     =   ( x   +   y ) 2   –   4 ( x   +   y )   +   1

Tại x + y = 3, ta có: A = 3 2 – 4.3 + 1 = -2

Đáp án cần chọn là: D